metric space

**resident911** · August 23rd 2012, 10:56 AM

Hi , i have this problem , i need help with this exercise

If b $\notin$ B[a,r] , prove that exist s>0 such that B[a,r] $\cap$ B[b,s] = $\emptyset$

Thanks

**Plato** · August 23rd 2012, 11:21 AM

Originally Posted by resident911

Hi , i have this problem , i need help with this exercise
If b $\notin$ B[a,r] , prove that exist s>0 such that B[a,r] $\cap$ B[b,s] = $\emptyset$

Please, please get in the habit of posting the meaning of notations that you use.
If $B[a,r]=\{x:d(a,x)<r\}$ the ordinary ball then the statement is false.
If $B[a,r]=\{x:d(a,x)\le r\}$ the ordinary closed ball then the statement is true.
Which is it? Or is it something altogether different?

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